1. Field of the Invention
The present invention relates to a light scanning device for scanning optical beam such as laser beam on a photosensitive medium in an image recording apparatus of an electrophotographic image recording type. More particularly, the present invention relates to a bearing device for supporting a rotating shaft of the light scanning device.
2. Description of the Related Art
There has been conventionally proposed an image recording apparatus of an electrophotographic image recording type such as a laser printer for recording an image on an output medium, with high speed, in accordance with image signals supplied thereto from an external computer device. The image recording apparatus generally includes: a charging device for electrically charging a photosensitive medium; a light scanning device for scanning image-bearing light beam on the photosensitive medium to thereby form a latent image thereon; a developing device for developing the latent image into a visible image; and a transferring and fixing device for transferring the developed image onto an output medium such as a paper and fixing the image thereto.
The light scanning device includes: a reflective mirror fixedly mounted on a rotational shaft; a bearing device constructed from a pair of bearings for rotatively supporting the opposite ends of the rotational shaft; and a motor for rotationally driving the rotational shaft about its rotational axis. The motor rotates the reflective mirror at several to ten thousands [rpm] to cause the reflective mirror to scan light beam incident thereon.
In the above-described conventional light scanning device, failing to mount the reflective mirror on the bearing device at a highly dynamically-balanced position causes the rotational shaft to vibrate or oscillate. Failing to precisely positioning the central axes of the reflective mirror, the rotational shaft and the bearing device also induces the vibration. The thus vibrating reflective mirror fails to scan image light beam at desired positions on the photosensitive medium.
It is generally known that a rotational body rotating or spinning about its rotational axis may excite two modes of natural resonances, i.e., cylindrical and conical modes of natural resonances where the rotational axis of the rotational body whirls or vibrates as shown in FIGS. 1A and 1B. In the cylindrical mode of whirl, the rotational axis remains parallel to its original or equilibrium position. In the conical mode of whirl, the rotational axis tilts about the center of gravity of the rotational body. The natural frequencies of resonances .OMEGA.y and .OMEGA.o for the cylindrical and conical whirls are expressed by the following equations (1) and (2), respectively: ##EQU1##
where S is a bearing stiffness of a bearing device which rotatively supports the rotational body, M is the mass of the rotational body, P is the polar inertia of the rotational body obtained about the rotational axis, I is the transverse inertia of the rotational body obtained about an axis that extends orthogonal to the rotational axis and passes through the center of gravity of the rotational body, L is the length of the rotational body along the rotational axis, and .OMEGA. is the rotational number (rotational speed) of the rotational body. The positive sign (+) denotes the forward whirl where the rotational body whirls in a direction the same as the rotational direction, and the negative sign (-) denotes the backward whirl where the rotational body whirls in the direction opposite to the rotational direction.
The bearing stiffness S of the bearing device is generally defined by a ratio between the displacement amount X of the rotational axis of the rotational body from its equilibrium position and a bearing restoring force Fx which the bearing device exhibits for restoring the equilibrium position. The bearing stiffness S is therefore expressed by the following equation (3): EQU S=Fx/X (3)
It is apparent from the above equations (1) and (2) that the resonant frequency for each of the cylindrical and conical modes of whirls is determined dependently on both the mass M of the rotational body and the bearing stiffness S of the bearing device. As the mass M decreases and as the bearing stiffness S increases, the resonant frequency for each mode of whirl increases. The resonant frequency for the conical mode of whirl also increases as the rotational speed of the rotational body increases.
It is further generally known that when the rotational body starts rotating from its rest, as the rotational number (rotational speed) .omega. increases to approach the natural resonant frequency .OMEGA. of each mode of whirls, the amplitude A at which the rotational body whirls or oscillates rapidly increases, as shown in FIG. 1C. When the rotational number .omega. equals the natural resonant frequency .OMEGA., the amplitude A of the whirls becomes extremely large. In other words, the amplitude A of the whirls becomes maximum or extremum. When the rotational number .omega. further increases from the natural resonant frequency .OMEGA. to recede therefrom, the amplitude A of whirls rapidly decreases. It is therefore apparent that when the rotational number is not equal to the natural resonant frequency but is close thereto, the rotational body oscillates at a large amplitude. In other words, when the rotational body rotates at a rotational number close to the natural resonant frequency, the rotational body is influenced by the corresponding natural resonance to be largely oscillated.
In the conventional light scanning device, the central axes of the reflection mirror, the rotational shaft and the bearing device are highly precisely positioned with respect to one another. A pair of highly rigid bearings of high bearing stiffness are used as the bearing device to forcibly restrain the oscillation or displacement of the rotational shaft. More specifically, because the rotational speed of the rotational shaft is not so high in the conventional light scanning device, the high bearing stiffness determines the resonant frequency for each mode of whirl to be considerably higher than the rotational number of the reflective mirror. It therefore becomes possible to forcibly restrain the rotational shaft from being influenced by any modes of natural resonant whirls.
Recently, however, the image recording apparatus is demanded to output images with much higher speed. This demand requires the light scanning device to rotate the reflective mirror with much higher rotational speed. In the above-described light scanning device employed with the bearing device of a high bearing stiffness, however, thus increased rotational speed approaches the natural resonant frequencies of the two modes of whirls. Accordingly, the rotational shaft is influenced by the natural resonances of the two modes to perform a precession action of a large amplitude. It therefore becomes difficult or impossible to stably rotate the reflective mirror with such a high speed.
One method has been proposed for stably rotating a rotor in a centrifuge in document entitled "Review of the Gas Centrifuge until 1962. Part 2: Principles of High-Speed Rotation" by S. Whitley (Reviews of Modern Physics, Vol. 56, No.1, January 1984.)
This method utilizes a bearing device of a very small value of bearing stiffness S, which in turn determines the resonant frequencies of both the cylindrical and conical modes of whirls to be considerably below the actual rotational speed of the rotational body. With this method, therefore, the rotational body can stably rotate with a rotational speed in a desired high speed range without being influenced by any resonant actions. This method is very effective to rotate or spin the rotational body with a high rotational speed, e.g., higher than several thousands rpm.
However, this method has the following problem. As described above, the low bearing stiffness determines the resonant frequencies of the both modes of whirls to low values. When the rotational body starts rotating or runs up from rest to full speed, the rotational speed has to traverse these resonant frequencies. At the time when the rotational number traverses the resonances, the rotational body excites the corresponding resonant actions to vibrate or whirl with a very large amplitude. The rotational body is largely displaced from its original position, which dangerously destroys the bearing device or wrecks the rotational body.